SummaryTombusviridaeis a large family of single-stranded, positive-sense RNA plant viruses with uncapped, non-polyadenylated genomes encoding 5-7 open reading frames (ORFs). Previously, we discovered, by high-throughput sequencing of maize and teosinte RNA, a novel genome of a virus we call Maize-associated tombusvirus (MaTV). Here we determined the precise termini of the MaTV genome by using 5’ and 3’ rapid amplification of cDNA ends (RACE). In GenBank, we discovered eleven other nearly complete viral genomes with MaTV-like genome organizations and related RNA-dependent RNA polymerase (RdRp) sequences. These genomes came from diverse plant, fungal, invertebrate and vertebrate organisms, and some have been found in multiple organisms across the globe. The available 5’ untranslated regions (UTRs) of these genomes are remarkably long: at least 438 to 727 nucleotides (nt), in contrast to those of other tombusvirids, which are <150 nt. Moreover these UTRs contain 6 to 12 AUG triplets that are unlikely to be start codons, because - with the possible exception of MaTV - there are no large or conserved ORFs in the 5’ UTRs. Such features suggest an internal ribosome entry site (IRES), but we found no conserved secondary structures. In the 50 nt upstream of and adjacent to the ORF1 start codon, the 5’ UTR was cytosine-rich and guanosine-poor. As in most tombusvirids, ORF2 (RdRp gene) appears to be translated by in-frame ribosomal readthrough of the ORF1 stop codon. Indeed, in all twelve genomes we identified RNA structures known in other tombusviruses to facilitate this readthrough. ORF5 is predicted to be translated by readthrough of the ORF3 (coat protein gene) stop codon as in genusLuteovirus. The resulting readthrough domains are highly divergent. ORF4 overlaps with ORF3 and may initiate with a non-AUG start codon. We also found no obvious 3’ cap-independent translation elements, which are present in other tombusvirids. The twelve genomes diverge sufficiently from other tombusvirids to warrant classification in a new genus. Because they contain two leaky stop codons and a potential leaky start codon, we propose to name this genusRimosavirus(rimosa= leaky in Latin).